If f(x)=x+3‾‾‾‾‾√ and g(x)=3x, find g(f(y)).

Given the functions \( f(x) = \sqrt{x+3} \) and \( g(x) = 3x \), we want to find \( g(f(y)) \).

### Step 1: Substitute \( f(y) \) into \( g(x) \).
We know that \( f(y) = \sqrt{y+3} \).

So, \( g(f(y)) = g(\sqrt{y+3}) \).

### Step 2: Apply the function \( g(x) \).
The function \( g(x) \) is defined as \( g(x) = 3x \).

Therefore, \( g(\sqrt{y+3}) = 3 \times \sqrt{y+3} \).

### Final Answer:
\[
g(f(y)) = 3\sqrt{y+3}
\]

Would you like more details on any specific part of this process? Here are some related questions you might consider:

1. How do you find \( f(g(y)) \) if \( g(x) = 3x \) and \( f(x) = \sqrt{x+3} \)?
2. What is the domain of \( g(f(y)) \)?
3. How does the composition of functions work in general?
4. What happens if \( f(x) = x^2 + 3 \) instead of \( \sqrt{x+3} \)?
5. How would you find the inverse of \( g(f(y)) \)?

**Tip:** When dealing with composition of functions, always evaluate the inner function first before applying the outer function.

Discover how to compute g(f(y)) using the functions f(x) = sqrt(x+3) and g(x) = 3x. Follow a detailed explanation with step-by-step solutions and understand the composition of functions concept. Suitable for advanced high school students and beyond.

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